THE BOOK--Playing The Percentages In Baseball

I have a question (which I now realize has two parts).

First, if you add up all the dollar values from fangraphs, is it similar to the total payroll of all ML players?

Secondly, if you use just the players who aren’t cost-controlled, does the aggregate fangraphs dollar value approximate the actual aggregate salary?

I would think that some players outperform their salary and some would underperform, meaning that if fangraphs’ dollar values were accurate, the totals would be similar

Right, if you add up all the guys with at least 6+ years of service, their aggregate Fangraphs salaries should pretty much match their actual salaries.

(Note that it’s not so simple, because of long-term deals.)

This is great.  It doesn’t really enhance my understanding of the numbers much, but enhances my ability to explain it to someone else by a lot.

Some random thoughts to add, I think a lot of people are confused by the process, since the 4.5 mil/WAR or whatever calculation is based on free agent salaries that have been given out in the past, but they see Placido Polanco sign for 3 years, 18 mil.  Even a very steep aging curve would put him at much more than 18 mil given that calcualation.  Jason Bay, on the other hand, will probably be paid way more than he’s worth using that calculation.

This also shows that paying 4.5 per win is usually not a good idea, as there are players who sign for much less than that.  You could probably sign Ben Sheets and Rich Harden for the cost of John Lackey, and be looking at LESS risk, because it would be fewer years and two players.

I understand what’s going on here, we’re taking what an average free agent gets per win, but distributing it correctly, based on actual production.  I’m just not sure how to explain that.  Here in Minnesota, people like to say that picking up Cuddyer’s option was a good move, because comparable left fielders make similar money.  Even if that was true, and I don’t think it is, that doesn’t mean that he’s worth that much money.

The only teams that can really pay that much for a Bay/Cuddyer type are teams with no other holes in their lineup. If you can sign Polanco for significantly less than Cuddyer, it doesn’t matter if that is the going rate for a mediocre outfielder, its still poor use of your money.

Anyway, just some ramblings about stuff I’ve been hearing (reading) lately.  If there’s a good way for me to explain that, let me know.

Right, if you add up all the guys with at least 6+ years of service, their aggregate Fangraphs salaries should pretty much match their actual salaries.

(Note that it’s not so simple, because of long-term deals.)

Just to clarify your statement (at least from my point of view): long-term contracts impact the first sentence more than you imply. Most players with value over $10 million a year will wind up with long-term deals because clubs can’t pay much more than that per year.  There is a lot of value above in players worth more than $10 million per year, so aggregate values for free agents won’t come close to aggregate actual salaries paid.

The exact process is laid out in the “Saber Rattling” thread from a few weeks ago, which is why I had to add the provision I add to my one line-response in this thread.

http://www.insidethebook.com/ee/index.php/site/comments/war_salary_and_service_estimating_dollars_per_win/

1. You figure the annual WAR over the life of the contract
2. You figure the annual dollars per win, with inflation, over the life of the contract.
3. You multiply the two numbers and add them up.
4. And that matches the salary.

And for the 2009 free agents with multi-year deals, in order for all that to match, the value in #2 is 4.7MM$ in 2009, and increase by 10% per year.

In 2010, it figures to be much less.

Actually, this was the thread:
http://www.insidethebook.com/ee/index.php/site/comments/how_much_did_the_2009_free_agents_sign_for_per_win/

I wonder if the “winner’s curse” drives up the salaries of marquee free agents somewhat. In the stock market, when several companies bid for a target corporation, the winner frequently overpays, and once the acquisition is completed, the acquiring company’s share price drops two-thirds of the time.

Let’s say five teams are serious candidates to bid for Mark Teixeira. The five teams independently assess his value using their internal metrics at $8m, $9m, $10m, $11m and $12m, respectively (ie team A thinks he’s worth $8m, team B thinks he’s worth $9m etc). This pegs his value at $10m +/- $2m. Who wins the auction? The team that bids $12m, and as a result they overpay by $2m and crank up the dollars per win level.

But then a smaller free agent comes on the market looking for a two-year contract. Only two teams are interested and he’s a one-dimensional player (eg a DH) who is easier to value. So, the two teams bid $2m and $2.1m, the $2.1m bid wins, but the overpayment is minor and the dollars/win value isn’t artificially inflated.

he produced at a level equal to what you would expect if you had spent $27 million in free agency a year ago.

Is that the question people want to answer though? Maybe these are my own expectations, but ... I’d imagine people just want to know how much the guy was worth last year.

If you add up total salaries paid to all players and divide by total WAR, wouldn’t you get a “contract-neutral” dollars per win (ie ignoring whether the player is a free agent etc) that could be applied to all players?

What a player is worth is essentially his WAR itself, as far as what value he provides to the team in the context of this question.  Asking how much that win value is worth in dollars is strictly a question of how the market values wins.  The market doesn’t set a valuation on cost-controlled players, so they’re salaries aren’t really relevant to answering that part of the question.  Using a dollar-per-win value derived from all players won’t tell you anything about how the market values wins or the cost of obtaining available wins and will pretty much just be an invitation to bemoan virtually every free agent signing, since they will all be valued much higher than such a figure would suggest.

I think that kind of figure would be less useful than the one in question and would probably just be misused more than anything.  I’m not a huge fan of the FanGraphs dollar values anyway, not because I think they’re wrong, but just because they’re so often misinterpreted and become a focal point of attacking the whole field of analysis, or else turn people off to these kind of stats who see something they assume is ridiculous (hopefully this article will help that), and a different figure derived from all players would just compound the misinterpretation and abuse of the stat.

Also, one of the advantages of the stat as is is that, while it’s not meant to predict salaries or forecast value, you can adjust the scale to see what a player would generally be paid for that expected production no matter what his service time.  You start with the market valuation, and then each year of arbitration tends to return a certain percentage of that.  Pre-arb players are even easier to value because they’re salary is whatever the team wants.  The market-valuation tells you something about value at all levels of service time.  Taking an average of everyone’s salaries together won’t really tell you anything about any level of service time.  It’s just an average of them all lumped together with no distinction between them or any kind of recognition of the reality of how the valuation of players is split across accumulation of service time.

Agreed, but when I look at a season like Ryan Howard 2006, I don’t really want to know what he would be worth if he were a free agent and if he put up the same production going forward. I just want to know what his production was worth in dollars. If you build a great salary model that accurately models service time, production etc, then maybe you conclude that Howard was worth $500,000 in 2006 (given service time etc). But is that what you really want to know? Maybe it is, but I have a feeling people would be more interested in knowing that he put up $8m of production (pulling a number out of the air).

Let’s say dollars per win for all players (ie total salary for all players divided by total WAR) is $4/win. If free agents are overpaid (relative to WAR) by 30% ($5.2/win) and non-free agents are underpaid by 30% ($2.8/win), then do you want to apply $5.2/win to all players? I’m not sure if you do, because total salary for the entire league is going to be higher than the actual salary paid. Your model has to work within the constraint of the overall size of the baseball economy.

If Ryan Howard was underpaid in 2006, then someone else (a free agent) was overpaid by the same amount. But if you assume that the free agent $/win is “fair value”, then you also assume that all free agents are paid fairly, which I don’t think is true.

If you apply $4/win, then estimated total salary = actual total salary. Sure, free agents will appear overpaid and the Ryan Howards of the world will appear underpaid, but that’s what we want to know, isn’t it?

If you want the salaries to add up, and for the model to work within the constraints of the overall economy of baseball, then you have to break it down by service time.  Lumping everyone together doesn’t tell you anything about how player valuation works in reality, and it doesn’t work within the constraints of baseball economics.

If you want to know what the market values wins at, you only look at the salaries set by the market.  I’m not sure what else you mean by what his production was worth in dollars.  The dollar worth is whatever the market values it at.  If he’s not available on the market, then that doesn’t really matter in terms of his actual salary, but that is how the market values his contributions.  Either you want a model that predicts his actual salary, in which case service time has to be considered, and the total salaries have to add up, or you want a model that values production in terms of dollars as the market dictates, in which case you won’t get a prediction of actual salary, and the salaries won’t add up, because the condition of having salary set by the market is not met by all players.  I’m not sure what good it does to answer how much you would expect him to be paid given his WAR if you could randomly assign him a service time or if you assume that there’s a 30% (or whatever it is) chance that you don’t have to pay for production at all and can just renew him at the league minimum no matter how good he is, which is more-or-less what lumping all players together does. 

The model doesn’t necessarily assume all free agents are paid fairly, it just looks at what they are paid.  The model doesn’t attempt to establish what is fair value, just what teams are paying for each available marginal win.

Think of it like gas.  There are 20 gas stations in town, charging between $2.40 and $2.70 a gallon.  Everyone in the world will know what you mean when you say that you get a good value from the $2.40 per gallon station, because it’s the best price among available sellers. 

That doesn’t say anything about the inherent value of gas, though.  To calculate its worth to you, you’d have to figure out the cost of living difference that a move to within walking distance of your office would cost, the value of being able to take your family places, etc…

No one cares about that.  When they talk about value, they mean relative price. 

Same deal with our $/win conversion.  It shows value as a relative price to what other players are selling their abilities for, and allows us to compare them on that basis.

I like the gas analogy, especially with the unpredictability of the price year-to-year.

Well, one way to find out what the market is willing to pay for wins is to look at free agent contracts. Another way is to look at the total dollars spent by the market for a given number of wins.

Pretend you’re going to buy four DVDs as Christmas gifts for your office mates and you have $60 to spend. You pick up two of the DVDs from the discount bin at a flea market for $5 each. You buy the other two from eBay for $25 each. Total outlay per DVD is $15.

Now, is a DVD worth $25 (the price set in an auction market), or is it worth $15? I’m not so sure if the $25 value from the auction market should be applied to all DVDs in all forms. The fact that you were able to pick up a few DVDs on the cheap meant that you had more capital available to spend in the auction market.

Likewise with baseball players. Because there is so much cheaply available talent, more capital is available for free agents, thus driving the price up. But if every player were made a free agent every year, I’m not so sure if $/win would stay at the same level. Why? Because where is the extra money going to come from?

Looking back to 2006, I get total payroll from B-ref of $2,321m and 930 wins above replacement (81 average wins minus 50 replacement wins x 30 teams), or $2.5m/win. If you make every player a free agent, owners are still only going to spend $2,321m on baseball players, and so the market value of $/win must fall to $2.5m.

Using $2.5m/win, Howard would be worth $17.4m in 2006, ranking 7th in the majors, which passes the sniff test.

In your DVD example, all of the DVD prices are set by the market.  You have cheaper DVDs, which presumably have a lower demand in the market, and more expensive DVDs that either have a higher demand or a lower supply.  You pay more for the more highly demanded commodity and less for the less highly demanded commodity, but you pay for both at a price set by the market for DVDs.  Given this model, DVDs are not analogous to WAR in baseball because DVDs are not a unit measure of quality of the product that has a pretty flat cost across all available units.  They are end products that come at varying prices based on their demand.  There are no units whose prices are not subject to the market.  There’s nothing similar to the baseball model.

A more relevant example that includes DVDs not bought at market values (but still isn’t really analogous to WAR) would be if you bought those same 4 DVDs for yourself at an average value of $15 each, and then stole 4 more DVDs (or got them from other people as gifts, or got them in some way where you dont’ pay for them).  Now, you paid $60 for 8 DVDs, but that doesn’t mean that they are only worth $7.50 each.  The ones you don’t have to pay for shouldn’t figure into the value of what you think DVDs should cost.  Likewise, talent you don’t have to pay for in baseball (i.e. players at the league minimum, where you are essentially paying for 0 WAR no matter what you are actually getting) doesn’t say anything about the market value of a win.

You’re sniff test on Howard seems to be based on the fact that $17.4m makes sense as the 7th highest salary in 2006.  That is not really what you want from this type of figure, though.  That would be true of a salary estimator, but not of a market valuation of WAR.  The sniff test should actually say that the top values in a given year should be well above the top actual salaries in a given year because of random variation.  Just as we always suspect that the top performing players in a given year outperformed their true talent and regress their projections to the mean, we know that the top performers in a given year will be higher than the top projections for that year, so no one will be paid to produce at a level as high as the top performers actually produce.  Given this, $17.4m for that high a performance does not pass the sniff test.  The market can’t be valuing wins that lowly and still be paying players at that high a salary level.

Including in a penalty that assumes there is a significant chance that you don’t have to pay for a player’s production at all is essentially serving as a regression to the mean that forces the values to a lower, regressed level.  Because of that, the top values you get end up looking more like a salary predictor because they factor in regression of the market value applied to the top seasons.  Now you are not looking at a value of what a player’s production was worth, but a regressed value that might end up approximating what he would be paid as a free agent going forward.

If all players were free agents, the number of available wins would go way up, and teams would probably have to pay less for them because of the increased supply.  That is not the reality of the market in baseball, though, so that’s not the scenario we strive to capture with this valuation.  The market doesn’t value players as if all wins in the game are up for grabs, it values players based on what is actually available.  That’s how the market value is determined, so that’s what we try to capture.

I disagree with this from Dave:

That’s why we write that he was “worth” $27 million. It does not mean that we think the Angels should have paid him $27 million, or that they should pay him $27 million now, but he produced at a level equal to what you would expect if you had spent $27 million in free agency a year ago.

If I’m not mistaken, the way that WAR$ are calculated is by taking 95% of a weighted average of the last three seasons’ WAR. 

http://www.fangraphs.com/blogs/index.php/win-values-explained-part-six

So, teams would pay 27 million on one year deal for Chone if he was projected to be worth ~6 WAR.  If the team knew that he was going to be worth ~6 WAR with no risk involved, I would think he would be paid a lot more.

If you make every player a free agent, owners are still only going to spend $2,321m on baseball players, and so the market value of $/win must fall to $2.5m.

Teams have a set budget.  If they have a 100MM$ payroll, they will spend to that.  If that means a subset of that group is going to get 4.5MM per win, while another subset is going to get .45MM per win, they don’t care.

If every player were a FA every year, then yes, 2.5MM per win will be the going rate.

Right, so under the existing system (in 2006), you have:

Total salary: $2,321m
Total WAR: 930
Dollars per win: 2.5

Under a system where every player is a free agent every year (ie a perfectly unconstrained free market), you have:

Total salary: $2,321m
Total WAR: 930
Dollars per win: 2.5

Given that dollars per win is identical under both scenarios, it seems pretty obvious that the going rate for free agents is an artificial value created by limited supply. So, while it may be useful for evaulating free agent signings under the existing salary structure, it is not a good way to put a dollar value on the production of the entire spectrum of major league players.

Dackle: agreed.  And, that’s the intent of the dollar values at fangraphs.

I’m not sure how the figure derived from how the market actually works is an artificial.  The supply of available wins is a part of market values, and I don’t see how ignoring that gives you a better idea of what the market value actually is.

The limited supply of wins in the market affects the price that teams have to pay to acquire wins.  When we use the dollars per win value, we are asking how much teams have to pay to expect that much return in wins.  I think that is a more relevant question than asking how much teams would have to pay for that much return if you assume there is a significant chance they don’t have to pay for a player’s production at all.

Say you sign a free agent.  Whatever his win value, you’ll have to pay whatever the market rate is (biases in the market notwithstanding).  Let’s just assume this is $4.5m.  Now say you want to know what he is actually worth.  If you use the $2.5m, you now decide that no matter how good he is, he is a net deficit of $2m per expected win.  So he has a negative surplus value no matter how good he is, unless you just severely underestimated his value when you signed him.  If another team called and offered you a replacement level player in a trade, you would want to take it every time because you are dumping a negative surplus value.  Obviously, that’s not how teams work.  We can, however, take the market value of $4.5m per win and calculate a surplus value from that, and then we have a surplus value that we can apply to trade offers and reach sensible conclusions.

The reason we calculate the figure based on how the market works given actual restrictions on the availability of wins is that it is a more useful figure.  We can use it to evaluate the actual market and to make decisions in the context of the market.  If we calculate the value based on all players and not just those on the market, we have a value that can’t be used for these things, which is fine as long as no one tries to apply that figure to a market analysis.  I’m not sure that a figure that loses all value when you try to apply it to the market it all that useful, especially when that is what most people are going to probably do with it.  The FanGraphs figures are already misused all the time, and using a value based on non-market contracts is just going to compound that problem.

The problem is that free agents aren’t the only way to buy talent. If I buy a baseball team and have $80m to spend on payroll, I don’t have to spend the free agent rate to fill out my team. The $/win I pay will be closer to total league salary divided by total WAR.

Here’s where Fangraphs salaries fall apart for me:

Actual major league payroll in 2009: $2,665m
Total of Fangraphs salaries: $4,657m (including negative salaries)

The difference is $1,992m ($66m per team). I don’t know many teams with an extra $66m kicking around to spend on players. I don’t really trust a salary model that assumes $1,992m will just magically appear from somewhere.

I think a cleaner approach would simply be to take the $2,665m actually paid and divide it up according to production. So Evan Longoria would be worth 7.2 WAR/930 league WAR x $2,665m = $20.6m. If I’m building a baseball team from scratch, that’s how much 7.2 wins are going to cost, from wherever I source them.

I agree though that if you are evaluating free agent signings or trades, a better baseline is the free agent $/win.

Congratulations, you’re the GM of the Dodgers, effective immediately.  You’ve got a pretty good team, but you need a second baseman.  How much are you willing to pay to acquire one?

According to your argument, you want to spend no more than $2.7 million per win, because that’s what a second baseman is worth.  Okay, show me who you’re going to get to play second base for $2.7 million per win and will help your team contend.

You can’t, of course, because your model doesn’t reflect reality.  You are missing every single cost that is not major league salary in player development - signing bonuses, overhead for scouting and player development, diminished value due to delayed return, etc…

Major league teams, of course, do not get to skip these costs.  Their choices are not “Spend $4.5 million on this free agent or spend $500,000 on this young, pre-arb guy”, becuase those pre-arb guys aren’t available.  They’re not part of the market supply.  They can’t be purchased. 

This is why your model is useless.  Your complaint about the FanGraphs number is that it doesn’t do something it’s not designed to do.  And it’s not designed to do what you want it to do because that would render it practically useless. 

Your model may be cleaner, but it would also be functionally worthless.

Dave - As I said above, it’s not entirely clear what the FanGraphs’ model does also.  You say that each WAR$ represents how much a team would have to pay to replace that players’ production, but that’s not really the case.  It’s more how much that team would have to pay to replace that production if they projected a free agent to do that.  If they knew that they would get that production, with no risk involved, they would almost certainly pay more.

Nick,

Read the bold faced part of what Tango quoted again.  “Produced at a level equal to what you would expect...”

For $27 million, you expect 6+ wins.  You don’t guarantee it, but you expect it. 

That’s what the metric is saying.  If you want to replace a player who had a 6+ win season and expect to get even production the next year, you need to spend $27 million to do so.  In that sense, Figgins performance was worth $27 million in 2009.

You’re right Dave, that makes perfect sense.  I’m not sure why I had a problem interpreting that.

I agree though that if you are evaluating free agent signings or trades, a better baseline is the free agent $/win.

And that’s what Fangraphs is doing.  That’s all it’s doing.  That you are trying to add it up at the league level is unfair because that’s not the purpose.

As Dave is saying, what the numbers represent is what you would have to have paid to get that level of production on the free agent market.  If you were guaranteed to get Greinke’s production, you’d pay 40MM$.

If Greinke were a free agent today, he’s get much less, say 25MM$ for a one-year deal, because he can’t guarantee that production NEXT year.

So, it has that practicalness to it.

Applying 2.5MM$ per win across the board serves little use.  In that case, you might as well just use WAR.

David, I agree in theory with everything you said in #23, except for your example of second baseman.

Given the contracts paid to Scutaro and Polanco, 2.7 per win for a 2B might be too high if anything.  Don’t you think a 5.5 million deal would get you Orlando Hudson or Felipe Lopez at this point?  It makes no sense to pay either any more than Polanco and Scutaro just got.

Plugging my free agent tracker:
http://www.baseballprojection.com/2010/freeagent2010.htm

Right, this year, the going rate for free agents is WAY down.

***

Rally: my suggestion is that you re-order by WAR, rather than Pos/WAR.  It’ll look cleaner.

Rally,

So far, this off-season has all the makings of a lowered $/win rate.  But, that still gets back to the point I was trying to make.  If Dackle’s response is that he’s going to get a free agent to fill the second base hole, then he’s subject to the market valuation, not the league average $/win value, and will have to pay what the going rate for wins in the market is. 

If the $/win rate has gone down this year, we’ll reflect that in the FanGraphs values.

My prediction is that Lackey, Bay, and Holliday are going to get the kind of money that implies a 4.5 to 5 million per win.

If the 3.5 million per win that we’ve seen so far holds, then Holliday will sign something like 6/70 and Bay will get simlar money to Figgins.  He’s already been offered 4/60 and turned it down.

That would put Lackey around 5/60.  If so the Angels better hold onto him.

Well, my point again it that free agency is not the only way to fill the gaps in a team. Half a dozen teams have a competent player at AAA ready to step in, and that should be factored into the replacement cost of the player.

I know what you’re going to say—AAA ballplayers don’t grow on trees, and that teams need to incur scouting and player development costs. Well, I don’t see how that adds up to the aggregate Fangraphs salary of $4,657m ($5,501m with the negative salary players zeroed out). Why? Because total MLB revenue last year was $5,819m, according to Forbes. There’s no way that they’re forking out $4,500-$5,500m for total player comp and development expense. They still have to pay for stadium operating costs, SG&A etc, and of course the owner wants to make a profit.

This is why I say you have to start with the total dollar value teams are going to pay for salaries ($2,665m) and then drill down from there. If you want to fully model different service classes and value free-agent eligible players at $4.5/win, great. That’s interesting and useful. But by doing that, you’re also going to have to model Ryan Howard 2006 at $355,000, and I’m not sure that’s what the average fan wants to know.

Nobody is claiming that the total of Fangraphs salary should match up to team total expenses.

I find what Fangraphs is currently doing a lot more useful than if they use 2m/win regardless of service time.  And I agree, showing someone like Howard 2006 at the league minimum is not very useful at all.

Do you want to model salary or do you want to measure market valuations?  They’re two entirely separate things.  We’re talking about market valuations here, which don’t have to add up to the total salary (and can’t really, given that many players are not really paid for production and aren’t subject to the market).

If you want to model salary, then you’re right, the salaries have to add up, and you’d have to break them down by service class, and you would have to model Ryan Howard around the league minimum.  As far as his market worth, that’s not interesting.  As far as modeling his actual salary, it is.

Knowing what a random player who may or may not be subject to the market averages given that you don’t know whether he is subject to the market or not is not really interesting for either question.  What interest is it to anyone that, if all you know about a player is that his WAR, he might cost $400,000 or he might cost $15m depending on his service time, and nobody values his production at $9m, but that that is the what the figure averages out to between what teams value him at on the market and the chance that they don’t have to pay for his production at all?  That doesn’t work as a market valuation tool or as a salary model.  What exactly are you trying to use the figure for, then?  For what questions or scenarios would it be more useful to use that figure than either a market valuation figure or a salary model?

Kincaid, the player “who may or may not be subject to the market averages” is not Howard, it’s his replacement.

The Phillies could tap the free agent market, or they could turn to their minor league system, or move a player from another position, or swing a trade etc etc. So the following…

If you want to replace a player who had a 6+ win season and expect to get even production the next year, you need to spend $27 million to do so.

... is just not true, and I’ll give you a familiar example to prove it. If AJ Burnett were projected at 3.1 WAR for 2009 (his actual total), the statement above implies it would cost the Blue Jays $14m to replace him (Fangraphs value). In fact, they more or less replaced him for $400,000 (Ricky Romero, 2.7 WAR).

As a result of these commonplace transactions, the replacement cost of a win is driven down below the free agent rate.

The true cost of a win to an MLB owner, given all of the available options to replace talent, is the leaguewide dollars per win.

Now you’re arguing about what replacement level is, which is an entirely separate argument.  If you think the availability of wins to be had freely by bypassing the market is higher than what is suggested by what teams are paying for wins that are available on the market, that’s an argument that WAR itself is off (and that teams are spending inefficiently), not the dollars per win figure.

That’s not particularly important to the dollars per win figure, though, because all that attempts to answer is what teams actually are paying on the market for wins, not whether they are doing so efficiently or not.

The Phillies could tap the free agent market

And pay market value.

or they could turn to their minor league system

Not if their minor league system doesn’t have any useful prospects in it.  You know how you get useful prospects? You pay a lot of money to sign and develop them, all of which you’re ignoring. 

or move a player from another position

In which case they haven’t solved anything, they’ve just changed their need. 

or swing a trade

Which requires paying the market price for available talent. 

Two of your four options are not real, and the other two require market price valuations. 

If AJ Burnett were projected at 3.1 WAR for 2009 (his actual total), the statement above implies it would cost the Blue Jays $14m to replace him (Fangraphs value). In fact, they more or less replaced him for $400,000 (Ricky Romero, 2.7 WAR).

There are many logical problems with this sentence.  Here are the main ones.  Please read them carefully and try to get what we’re telling you. 

1. Burnett and Romero did not have equal projections prior to 2009.  That their performance ended up being fairly similar tells us nothing about what a team should have valued them at a year ago. 

2. Romero did not cost the Blue Jays $400,000.  He cost them $2.4 million to sign in 2005, then required additional funding to develop him into a major league player.  All told, the Blue Jays have invested ~$3 million in Romero to date.  And, here’s the kicker - that investment only gave them a small chance of getting a good return on that investment. 

To figure out the true cost of having a player like Romero in the system, you have to calculate the costs of all the prospects the Blue Jays have invested in.  The busted prospects, the high picks who never pan out, the guys who blow out their arms in the minors… they’re all part of the pool that Romero came from, and they all cost money to sign and develop.  You are ignoring those costs, which dramatically skews the perspective of whether a team should pay market value or try to develop a cost controlled player. 

The true cost of a win to an MLB owner, given all of the available options to replace talent, is the leaguewide dollars per win.

No.  No.  No.

Just pitching in, as someone who used to do a lot of salary analysis.  I’m not a big fan of the Tango/Fangraphs approach in terms of future value, but it does do exactly what Dave describes for interpreting past value. My beef: Given that it’s just a straight multiplication of WAR, I don’t find it all that informative and I think it can be (and frequently is) misinterpreted.

David, reread post 32. There’s no way that a league with revenue of $5,819m can support a “fair value” of $4,500-$5,500m, as Fangraphs’ salaries imply. That $4,500-$5,500m presumably includes actual salaries paid ($2,665m) plus player development costs.

Your value for Romero of $3m still doesn’t come anywhere close to the $14m+ Burnett was presumably valued at prior to the 2009 season. This, and many other roster decisions like it, drive down the cost of a win.

Given that we can’t truly know how the Blue Jays were going to replace Burnett, our best guess is a weighted average of their options. And that’s exactly what the leaguewide dollars per win is—a weighted average of the cost of a win, given the different options of paying for it.

You guys speak of the free agent value as being the only true fair market price and an accurate measure of the funds a team is willing to pay for a win. But it is not a “free” value. It is a function of limited supply. In fact, you could probably calculate the free agent $/win in reverse without even knowing what the contracts were! Take total salary and total wins, subtract salary and wins for cost-controlled players, and from the remaining salary and wins you can derive the free agent $/win.

Your model works for one or two players in isolation, but it falls apart when you extend it across the entire player universe, ie by making every player a free agent. If that happened, $/win wouldn’t remain at the free agent level. It would revert back to league dollars per win, because there are a fixed number of wins available and a budgeted number of dollars to spend (ie total league salary).

I think what causes some of the confusion with the Fangraphs salaries is that because every player is assigned a dollar value, it does in fact give the impression that the entire league is worth the free agent $/win, which of course can’t be true unless you can explain where an extra $2b comes from.

FanGraph’s dollar values are not salaries, and they do not imply that the total market value of all players combined equals the total salary of all players combined.  Why do you keep repeating that criticism when a basic understanding of what the numbers mean reveals that that is entirely irrelevant?  Also, “fair value” is a term you are making up in this discussion.  All the dollars per win figure cares about is what the market value actually is, not whether it is fair or not.

“Your model works for one or two players in isolation, but it falls apart when you extend it across the entire player universe, ie by making every player a free agent. If that happened, $/win wouldn’t remain at the free agent level. It would revert back to league dollars per win...”

That last sentence is not true.  Both models (FG’s market value and the total salary divided by total WAR) fall apart in a universe where every player is a free agent.  Neither one describes that environment.  That’s not a particularly important criticism, though, because that universe does not exist in the reality of the market, so it’s not particularly important in a practical sense to describe it.  If you wanted to know what teams would pay for a win in that hypothetical market, there would be no way to test your model, but the dollars per win figure would end up somewhere between what it is now and the total salary divided by total WAR in the league.  The current market figure would be too high and the current total salary/total WAR would be too low.

The extra $2b doesn’t come from anywhere.  Teams don’t have to pay it because of the glut of players who are not available on the market.

There is a good deal of confusion about the FanGraphs dollar values (for instance, after them being thoroughly explained throughout this thread and the article linked, you still call them salaries, which they are not, and insist that they must add up to the total salary of all players, which is not true).  That’s an issue.  Replacing those figures with figures that completely fail to capture the market and misvalue what teams are paying to acquire wins would create much more confusion and abuse of the numbers.  More confusion and less practical use do not constitute an improvement.

Your model works for one or two players in isolation, but it falls apart when you extend it across the entire player universe, ie by making every player a free agent. If that happened, $/win wouldn’t remain at the free agent level. It would revert back to league dollars per win, because there are a fixed number of wins available and a budgeted number of dollars to spend (ie total league salary).

This has always been my position, and I said as much.

You guys speak of the free agent value as being the only true fair market price and an accurate measure of the funds a team is willing to pay for a win. But it is not a “free” value. It is a function of limited supply.

I never speak of it that way.  And I’m one of the few that puts free in “free” quotes.  I’m entirely in agreement that this free agent market has nothing to do with free anything.

It’s the “perpetuity-rights terminated market”.

***

The dollar values are ONLY if you introduce ONE of the 1800 players into this “Free” agent market, and showing what the value of his production would be worth in the “perpetuity-rights terminated market”, if you hold the other 1799 players constant.

That’s it.

David, reread post 32. There’s no way that a league with revenue of $5,819m can support a “fair value” of $4,500-$5,500m, as Fangraphs’ salaries imply.

It’s a good thing that we’re not claiming it should then.  Seriously, you keep repeating this like it means something.  It doesn’t.  Your criticism of the model is that it doesn’t work in an alternate reality.  No one cares about that hypothetical but you. 

Your value for Romero of $3m still doesn’t come anywhere close to the $14m+ Burnett was presumably valued at prior to the 2009 season.

I’m trying to be nice, but this part should be really easy to grasp - Burnett and Romero did not have equal projections a year ago.  By this argument, no one should pay anyone any money, because Ben Zobrist put up an 8 win season for the league minimum.  Every team should have just acquired him instead of doing anything. 

And that’s exactly what the leaguewide dollars per win is—a weighted average of the cost of a win, given the different options of paying for it.

No, it’s not.  I don’t know how many times we can drive this point home and you ignore it, but you’re skipping over tremendous costs and pretending that they don’t exist. 

Take total salary and total wins, subtract salary and wins for cost-controlled players, and from the remaining salary and wins you can derive the free agent $/win.

Ding ding ding! This is how it actually works in the real world.  That’s what we’re modeling, because that’s what happens. 

Your model works for one or two players in isolation, but it falls apart when you extend it across the entire player universe, ie by making every player a free agent.

When baseball gets around to abolishing the current state contracts, we’ll change the model.  Until then, you might as well say that it doesn’t work because it doesn’t project climate change or what kind of food you’re going to have for lunch.

OK, I’ll give you the benefit of the doubt re: player development costs. If Fangraphs’ dollar values add up to $4,660m and actual salaries are $2,660m, then that implies that embedded player development costs are $2,000m. Given league revenue of $5,819m and operating income of $501m, that leaves $5,301m for player development, stadium operating costs, interest on debt, owners’ profit etc. I doubt that player development accounts for $4,660m. At a more reasonable $4,000m, the value of a win would fall to about $3.85m, but for the sake of argument, let’s assume that total salaries + player development costs = the total Fangraphs value of $4,660m.

In that case, at $4.5m/win, the value of a free agent might be $4.5m salary + $0.0m embedded player development costs. A cost-controlled player might also have a value of $4.5m/win, but that might break down as $1.0m salary + $3.5m embedded player development costs.

That’s fine if you want to assess the salary of a free agent, but I can’t really see how it’s useful for the rest of the league. For guys like Ryan Howard in 2006, the fundamental question seems to be—how much would the guy make if paid fairly for performance. For that, the answer is league $/WAR x player WAR (ie $17.4m). The reason is that no matter what the underlying compensation structure is, teams are still only going to budget $4,660m for overall player comp, and of that the $2,000m of player development expenses will remain fixed, and so will the $2,660m in salaries. So, Howard generates 7 WAR in a 930 WAR league, so he deserves 7/930ths of the $2,660m salary pie, or about $20.0m. In 2006, the pie was $2,321m, so his fair value then was $17.4m.

Another basic question is “how much would he make if he became a free agent after the 2006 season”. Fangraphs says that dollar values are “WAR converted to a dollar scale based on what a player would make in free agency”. That’s awfully close to saying at Zobrist would make $39.1m in free agency. But we know that to estimate his free agent salary, we still have to break out the spreadsheet and project WAR and salary inflation.

The way Fangraphs dollar values have been described implies a less fundamental question that contains a lot of conditionals (I’m not picking on anyone in particular here)—IF he guaranteed his performance, IF he were the only free agent in the league, IF he signed a one-year contract, IF player development costs + salaries = free agent costs etc. 

However, I’m not going to criticize Fangraphs for not doing what I think it should be doing. Just trying to shed some light on some of the reasons why it can be misinterpreted and how it can be improved.

I think we’re on the same page now.

I’d make the conditionals:
IF he guaranteed his performance,
IF he were the only ADDITIONAL free agent in the league,
IF he signed a one-year contract

Yes, that’s what it’s doing.

This is a bit of a tangent, but I think the total value that WAR assigns to hitting, fielding, and pitching raises interesting questions.  In 2009, according to Fangraphs the average team had 20 WAR from hitters, 15 WAR from pitchers, and 0 WAR from fielders.  (Actually, the position adjustment averaged -1.2 WAR per team, but I assume that’s just a glitch.) Position players get 56% of the WAR overall. 

Personally, I agree with the zero aggregate value for fielding (but Tango has disagreed with that in the past).  But if you give fielding zero total value, then I have a hard time seeing how position players can have more value than pitchers.  We know that the total variance for offense and defense is the same, so if we stipulate total fielding value = zero, how can hitters then can have more value than pitchers?

I don’t think you can separate hitting and fielding WAR just from FanGraphs’ tables.  Both components are just measured relative to average, and the replacement bonus is added in separately and makes no attempt to distinguish between the two.  As far as FanGraphs is reporting, teams would just average 0 wins from offense, 0 wins from fielding, and 20 wins from replacement bonus for non-pitchers, with that replacement bonus covering both offense and defense.

Right, what Kincaid is saying.  I don’t know where you are seeing that Fangraphs has 20 WAR for offense and 0 for fielding.  That makes no sense to me, and if Fangraphs is showing that, then I’ll tell David that he is wrong about that.

Otherwise, the allocation of the replacement level of 20 WAR per team does not distinguish between the hitting and fielding portion of a non-pitcher.

Tango/Kincaid:  Yes, the 20 WAR I attributed to hitters is called “replacement.” But how is that calculated?  The Fangraphs glossary cites a THT article by Sean Smith, in which he arrives at replacement run estimates ENTIRELY by looking at replacement players’ offensive production.  And that is certainly a common way to measure the difference between a replacement player and an average player.  If the WAR replacement factor is incorporating fielding, there is no indication of that AFAICT. 

If WAR were going to allocate positive net value to fielders, wouldn’t it make sense to do that by having a positive aggregate value for the position adjustments? 

And in any case, doesn’t the evidence generally suggest that replacement players in fact do provide league-average defense? (Maybe a little worse at SS, a bit better at some other positions.) So in fact an average MLB team and a team of replacement players would probably provide roughly equivalent defense.

Guy, no, the replacement-level players provide below-average fielding.

Regardless, I see no reason to distribute the 20 runs between hitting, fielding, baserunning, or whatever other aspect of player performance there is.  A player is a player.  And the minimum level of talent to play in MLB is roughly 20 runs below average per full season.

I think Replacement level is just calculated from looking at the free agent market and seeing at how far below average teams stop paying for wins.  If you calculated a linear salary model based on WAA instead of WAR, you would end up with the same line, and the intercept would be your replacement level.  That calculation includes both hitting and fielding as long as you use both in calculating WAA.

Replacement level players can be anywhere on the fielding spectrum.  A player can be replacement level because he is an average fielder and a really bad hitter, or he can be a decent hitter and a really poor fielder, or any combination of hitting and fielding skills that add up to replacement level.  Theoretically, you could have an average team and a team of replacement level players that would provide roughly equivalent offense if the latter were filled with really poor fielders (like poor first basemen at every position).  The only thing defining replacement level is the overall value, whether that comes from fielding or offense.

I don’t think Sean’s article is an independent derivation of replacement level so much as it’s a verification of Tango’s numbers using a different approach.  There are some differences, which Tango speculated could be from biases in the fielding talent of replacement players at each position:

http://www.insidethebook.com/ee/index.php/site/comments/replacement_level_using_forecasted_players/

Sean’s article also doesn’t necessarily suggest that the fielders in the sample are average as a group, just that if they are all below average, they are below average by the same amount at each position.  This is because he started off with Tango’s replacement levels in mind and then kept pushing the quality of hitters down until the numbers closely matched.  When he started off with the 61st best hitter at each position, they hit too high to be replacement level, so he started looking at players outside the top 75 or 90.  That could be because the top so many players worse than the worst Major Leaguers aren’t readily available, or it could be that the 61st best players at a position also field worse than average, so replacement level players really do hit at that level, and you only have to keep looking at worse players when you force the replacement level to come entirely out of offense.  Using offensive numbers alone and forcing them to fall on the same scale as the numbers combining both offense and defense will give you the same results as long as there is no positional bias in how good or bad the fielders are relative to average, you just might be looking at different sets of players as replacement level.

Kincaid/Tango:  of course any individual replacement player can fall anywhere on the fielding spectrum.  But the point is that on average, and in the aggregate, they are league-average fielders.  I looked at the Fangraphs data for non-catchers this year, and if you take the top 210 players as regulars, their UZR/150 is zero.  Same for the non-regulars.  The correlation between UZR and defensive innings is zero (slightly negative).  Backups are equally talented fielders as starters, and if that’s true it’s impossible to imagine that replacement players are materially worse fielders than the backups.  (If 2009 is an abberation, and the backups are usually inferior fielders, then please set me straight).  When Nate Silver did his study of replacement players, he also found that they were league-average fielders, except SSs were a little worse, 1Bmen a bit better 9and since he only looked at players over 27, he probably underestimates the fielding talent of all replacement players). 

As for “why bother” to allocate the runs between hitting and fielding, there are a couple of reasons.  One is to validate that the 20 runs is correct.  We don’t have replacement teams to observe, only replacement players.  The only way to establish replacement level is to measure their hitting and fielding abilities.  If they are -20 as hitters but also below-average on fielding, the -20 total is wrong; if they are -16 as hitters but in fact average fielders, again the overall -20 is mistaken.

Second, it helps us figure out if the relative allocation of WAR to pitchers and non-pitchers is correct.  If we don’t know whether the fielding portion of the -20 is 0%, 10%, or 50%, then we don’t know if the 56%/44% position/pitcher split makes sense.

Looking at BaseballProjection’s data from 1955-2008, players above replacement level in a season are, in general, above average at both batting and fielding in that season.  The following are the average runs above or below average (position-neutral numbers) per 20 replacement runs in batting and fielding for players above 0 WAR, 1 WAR, and 2 WAR:

+07 bat +3 field - 0+ WAR
+14 bat +2 field - 1+ WAR
+19 bat +3 field - 2+ WAR

You don’t need to break down replacement level between hitting and fielding for that validation.  All you need to know is what the total batting and fielding level of the players is.  If it’s -20, however that breaks down, then -20 is correct.  If that breaks down as -20 and 0 or -16 and -4 for replacement levels on average, that’s not particularly important.  If you have a -20/0 player and a -16/-4 player, it’s the same thing.  You don’t really care if that is a typical breakdown for replacement level or not, just that it is replacement level.  All you need replacement level for is to compare to a player’s overall contributions, batting and fielding combined.

If the average replacement level player does happen to be average on defense, though, I don’t think that even makes any difference.  The sum of offensive value doesn’t have to equal the sum of defensive+pitching value.  Replacement level is dependent on scarcity, so if offense is harder to get, the replacement level will be lower for non-pitchers than for pitchers.

Say that you knew that pitcher WAR did equal non-pitcher WAR.  Then, all of a sudden, half of the non-pitchers decided they can make more money playing cricket and quit baseball.  The replacement level for non-pitchers will now be lower, so now the non-pitchers will be more valuable than the pitchers just because their production is harder to come by.  It wouldn’t have anything to do with the allocation of talent between offense and defense for those players changing.  I don’t see anything stipulating that offensive WAR has to equal defensive WAR, because the replacement levels for pitchers and non-pitchers don’t have to be the same.  Knowing how a typical replacement level player breaks down between offense and defense doesn’t tell you anything about whether or not the 56/44 split makes sense.  You would just have to know what the replacement levels are for pitchers compared to non-pitchers to do that.

If it’s -20 / 0 or -18 / -2 or -16 / -4, then it’s -20 regardless.  That’s why it doesn’t matter.

Kincaid:
You say “If it’s -20, however that breaks down, then -20 is correct.” Well, yes, but that’s tautological.  HOW do we know it’s -20, other than measuring the hitting and fielding skills of these players? 

Of course players with positive WAR have a positive fielding value—you have a huge selection bias there because you’re looking only at players how had positive value.  (What do you get if you look at all players between -1 and +1 WAR?).  What’s revealing in your data is that the fielding value remains constant:  great, average, and weak players all field the same.  Doesn’t that tell you something? 

I agree that offensive value and defensive value need not be identical, theoretically speaking (I believe Brian Burke’s data suggests NFL teams vary more in offensive talent than defensive talent).  But since the variance in team RS and RA in MLB is always nearly equal, I think in fact they are.

"If it’s -20 / 0 or -18 / -2 or -16 / -4, then it’s -20 regardless.”

But this is circular.  If you don’t know or care whether these players are 0, -2, or -4 on defense, how can you possibly know they are -20 overall?  (Feel free to answer with link if appropriate).

I posted before seeing Kincaid/52.  Ditto his entire post.

You simply figure out what everybody’s production is relative to average.

Line them all up.  The replacement level is the 421st best nonpitcher.  That’ll be around -20 runs per full season.  And the replacement level is the 330rd best pitcher (or 390 and 360).

Replacement level is really un-needed except for salary valuation.

Isn’t that pretty much the same thing you did?  You took the top 210 players from FanGraphs and looked at their fielding value and hitting value, which is the only reason I posted those numbers (you were asking if the same kind of thing returns the same results for years besides 2009).  That’s the same selection bias. 

Fielding value doesn’t remain constant.  It goes down for players below replacement level.  Also, it’s impossible to know how constant they are in those samples since there is a lot of overlap between them.  How consistent fielding levels are on average across WAR levels doessn’t really tell you anything, though.  Whether it’s the same across levels or whether it goes down closer to replacement level, that doesn’t have anything to do with what replacement level is.  As far as we know, if defensive talent in the Majors doesn’t go down as you near or dip below replacement level, it could just be another selection bias that, given a choice between two similarly valued players, teams prefer to select near-replacement level players who are solid defensive players with no bats for their bench because they think those players fill a role better than the other near-replacement level options whose bats may be considered a redundancy on the roster.

If you really want to know what a typical replacement level fielder’s value is, you could do the same type of thing as Sean did by looking at the actual players in the replacement level pool (not necessarily players in the Majors who perform at 0 WAR), but include defensive projections as well as offensive.  I still don’t think that really makes any difference, other than just if you want to verify the theory of replacement level or position adjustments or whatever against the total value of the available replacement level pool of players instead of just looking at batting value with the assumption that there’s no fielding bias.

How does knowing how the allocation of hitting and fielding skills break down on average tell you any more about what replacement level is than just knowing what they are combined?  It’s tautological either way, because once you break them down, the only thing that matters is still what they add up to.  We “know” what replacement level is because we define it by how far below average teams are still willing to pay for wins on a linear scale, so whatever the observed value of that definition is is replacement level.  We do that by measuring the hitting and fielding skills of players, but combined together.  How they break down tells you nothing additional about replacement level.  It does nothing more than trying to break down offense into on base ability and slugging and base stealing or fielding into range and arm and sure-handedness.  It’s just breaking down the same 20 runs into various allocations that can be different for any player without making any difference on replacement level.  The only way you confirm it is by looking at how all the components add up, regardless of how they are allocated. 

You wouldn’t say that you can’t just use fielding value, because how can you know fielding value without measuring and then adding up all the separate components.  Just taking the sum of the fielding value without breaking it down does the exact same thing, and considering how the components of fielding value break down doesn’t add anything to knowing what replacement level is.  It’s the same with breaking down the +20 between offensive and defensive components.

"You simply figure out what everybody’s production is relative to average. Line them all up.  The replacement level is the 421st best nonpitcher.”

Tango:  Fine so far. But now what?  Don’t you have to measure the 421st player’s offense and fielding?  How else can you arrive at -20?

*

Kincaid:
No it’s not the same thing.  I selected players based on playing time (defensive innings), not based on performance—totally different.

“If you really want to know what a typical replacement level fielder’s value is, you could do the same type of thing as Sean did by looking at the actual players in the replacement level pool.”

That’s what Nate Silver did.  The replacement players were league-average fielders. 

“We do that by measuring the hitting and fielding skills of players, but combined together.”

Who does that?  And how?  I’ve never seen a metric for the combined hitting and fielding performance of a position player, only separate metrics for hitting and fielding.  What are you talking about here? 

*

Look, I agree that if we know -20 is the right number, then our estimate of players’ value doesn’t depend on knowing much of that is fielding.  But I don’t see how you can get that # without measuring fielding.

I think the problem here is that WAR does implicitly accept the notion that aggregate fielding value is zero.  I suspect most fans who use it interpret the replacement level adjustment to be based on the offensive gap btwn average and replacement players.  But still people just don’t feel comfortable saying “the total value of fielding is zero.”

The fact is that fielding talent is vastly less scarce than hitting talent.  There are plenty of guys in the minor leagues who could win a gold glove in MLB; there are not guys in the minors who could win a batting title or lead the league in wOBA.  But for some reason, people don’t like to acknowledge this reality, I suppose because it seems to imply that defense doesn’t matter (which is not true at all).  Very curious.....

The number is not derived without fielding, so that’s not an issue.

“I’ve never seen a metric for the combined hitting and fielding performance of a position player, only separate metrics for hitting and fielding.  What are you talking about here?”

WAR

“You simply figure out what everybody’s production is relative to average. Line them all up.  The replacement level is the 421st best nonpitcher.”

Tango:  Fine so far. But now what?

That’s it.  Why go further?

I think the problem here is that WAR does implicitly accept the notion that aggregate fielding value is zero.

And the aggregate offensive value is also zero.

The reason that the average team has a negative positional adjustment is because of the DH. NL teams should have positional adjustment reconcile at close to zero (not quite - because of things like lineup order, due to the distribution of fielding adjustment by PA you will have some oddities involving position, but nothing really notable).

League hitting won’t exactly reconcile at 0, because league average is computed (I think) with pitchers excluded. Since there’s no positional adjustment for pitching, FG WAR for an NL team is going to be somewhat lower than an AL team, due to the pitcher hitting. That’s slightly offset by the DH penalty to AL teams, but IIRC it’s still a net negative for the NL.

As for:

“I agree that offensive value and defensive value need not be identical, theoretically speaking (I believe Brian Burke’s data suggests NFL teams vary more in offensive talent than defensive talent). But since the variance in team RS and RA in MLB is always nearly equal, I think in fact they are.”

Is that true? I guess it depends on your value of almost. The population SD for team offense in 2009 was .45, compared to .40. Yeah, it’s only one year - I’m pretty sure that reflects the historic reality. (I’m not at my computer right now - I’ll check this later.)

That’s in runs per game, in case you were wondering.

Looking at 1952-2009, the SD of runs per game is nearly identical in offense and defense - .57 for offense, .59 for defense. Hrm.

Is that really important?  We know that part of the variance in team runs allowed is because of defense and that it’s not all pitching. Non-pitchers still have an effect on the variance of both sides of the ball, so that doesn’t necessarily imply that the sum of all pitching value should yield the same replacement level as the sum of all non-pitching value.

"Looking at 1952-2009, the SD of runs per game is nearly identical in offense and defense - .57 for offense, .59 for defense. “

I’ve found similar results in the past.  The standard deviation tells you the percentage that is offense and defense.  Pretty much 50/50.  This is true in all sports.

Defense is made up of pitchers and nonpitchers.  Offense is made up of nonpitchers (for the most part).

Regardless, this has nothing (directly) to do with the issue here.  You list your top 400 nonpitchers, you list your top 350 pitchers, and that’s it:

http://www.tangotiger.net/talent.html

Kincaid/Tango:  I’ve asked several times for evidence that the total replacement/average gap is 20 runs, but you still haven’t provided any.  And I’ve asked how it is that you could measure this gap without somehow measuring offense and fielding separately, and again I get no answer (except “WAR,” which is of course totally circular.) So I’m sorry to be stubborn, but I ask again: 
1) how do we know that the 421st player is 20 runs worse than the 210th? 
2) And how can you measure that without measuring hitting and fielding separately?

*

Colin:  In football, I don’t think you can look only at total points scored and allowed, because they aren’t independent.  An offense with the lead will run late in the game, trading points scored for time consumed.  So great teams could score more runs if their goal was to maximize scoring. 

If you look at Brian Burke’s data, it suggests there is more variance on the offensive side in terms of yards per pass attempt, yards per run attempt, and interception rate.  But I don’t know if this has been true in years past.  My football knowledge is very limited, I’m just noting that NFL could be different.

http://www.advancednflstats.com/2009/12/team-efficiency-rankings-week-14.html

Guy: I am saying that you DO measure them separately… but relative to average (plus a positional adjustment).  And the 400th best nonpitcher, relative to average, is 20 runs below average.

So, I am simply repeating myself each time.  Clearly, there’s something being lost in the translation.

Tango:  OK, we’re on the same page.  And when you do measure them separately, I’m guessing you get something like -16 hitting and -4 fielding on average (with a lot of variation, of course).  Is that right?  And if so, can you post link to article/thread where you arrive at the negative fielding value?

More like -18/-2 I’d say.

I have a few threads in this blog from probably 2 years ago on the subject.  It’s under the “fielding” category.  I’ll find it for you…

Here’s one:
http://www.insidethebook.com/ee/index.php/site/comments/replacement_level_fielding1/#4

If we focus on the “Rest”, fielding-wise, they are about .04 plays, or .03 runs, worse than average, while hitting-wise, they are .13 runs worse than average.  That makes them .16 runs worse than average, per game.  Multiply by 162 GP, and you get -26 runs, or roughly -2.4 wins.
...
We see here that the replacement-level DH (which of course includes guys like Manny Ramirez) is -.03x162=-5 runs, or -0.5 wins.
...
So, in my previous post, when I was trying to figure out the replacement level nonpitcher team, I should now say:
-2.4 x 8
-0.5 x 1 x (14/30)
= -19.4 wins
= .380 replacement win% for nonpitchers

Hmmm… seems my .380 that I’ve been using is probably pretty good to begin with.

There’s also a “Guy” that shows up in post 13.

***

There was a study I always wanted to do.  And, reading that thread, I see that I DID it two years ago:

As you can see, the “Rest” hitters are pretty horrible, at -.237 runs per game (4.3 PA).  At 162 GP, that’s -38 runs.  But, we’ve got selective sampling issues.  PA don’t exist in a vacuum.  The better you hit, the more you’ll play.

What you should do is find out how the guys who are in the “Rest” category in year x did in year x+1.  So I did.

There are, by definition, 210x6=1260 “Starters” from 2000-2005.  How’d those guys do in the year after?  22 did not play in the following year, and 14 had less than 50 PA.  Of the remaining 1224, their (simple average) runs per game was +.02.

Of the 937 (of 1260) Bench players, they were -.10.

Of the 314 bench players in year x (with at least 30 PA in each year), their (simple average) runs per game was -.135.

On top of which, the bench players were around age 27 as well (as many guys under 27 as over 27).  This is unlike the starters and bench group which averaged 29.6 years.  So, we don’t have an aging issue to contend with.

I think it’s fair to call the offensive talent level of replacement-level players as -.135 x 162 = -22 runs.

Add in the likely minus couple of runs, and we end up with around -25 runs as the overall replacement level (-2.3 wins).

That’s .380 win % as the replacement level for nonpitchers.

Any way you want to slice it, we always end up in the same place.

That was a great thread by the way.  I recommend all to read it.

There’s also this thread:
http://www.insidethebook.com/ee/index.php/site/comments/replacement_level_fielding/

Overall, the average regular fielder is around +2 plays better than the average bench player. (Note that the bench player will include regulars playing out of position.)

Whoops, was going to drop that into the discussion of Sky’s article—the $6.5-7.5m refers to Sky’s finding.

[Ed note: I moved it there.]